TY - GEN A1 - Weiser, Martin A1 - Deuflhard, Peter A1 - Erdmann, Bodo T1 - Affine conjugate adaptive Newton methods for nonlinear elastomechanics N2 - The paper extends affine conjugate Newton methods from convex to nonconvex minimization, with particular emphasis on PDE problems originating from compressible hyperelasticity. Based on well-known schemes from finite dimensional nonlinear optimization, three different algorithmic variants are worked out in a function space setting, which permits an adaptive multilevel finite element implementation. These algorithms are tested on two well-known 3D test problems and a real-life example from surgical operation planning. T3 - ZIB-Report - 04-01 KW - affine conjugate Newton methods KW - nonconvex minimization KW - nonlinear elastomechnics KW - cranio-maxillofacial surgery KW - soft tissue simulation KW - multilev Y1 - 2004 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-7768 ER - TY - GEN A1 - Schiela, Anton T1 - A cubic regularization algorithm for nonconvex optimization in function space (in preparation) N2 - We propose a cubic regularization algorithm that is constructed to deal with nonconvex minimization problems in function space. It allows for a flexible choice of the regularization term and thus accounts for the fact that in such problems one often has to deal with more than one norm. Global and local convergence results are established in a general framework. Moreover, several variants of step computations are compared. In the context of nonlinear elasticity it turns out the a cg method applied to an augmented Hessian is more robust than truncated cg. T3 - ZIB-Report - 12-16 KW - nonconvex optimization KW - optimization in function space KW - nonlinear elasticity Y1 - 2012 SN - 1438-0064 ER - TY - GEN A1 - Lubkoll, Lars A1 - Schiela, Anton A1 - Weiser, Martin T1 - An optimal control problem in polyconvex hyperelasticity N2 - We consider a shape implant design problem that arises in the context of facial surgery. We introduce a reformulation as an optimal control problem, where the control acts as a boundary force. The state is modelled as a minimizer of a polyconvex hyperelastic energy functional. We show existence of optimal solutions and derive - on a formal level - first order optimality conditions. Finally, preliminary numerical results are presented. T3 - ZIB-Report - 12-08 KW - polyconvex elasticity KW - implant design KW - optimal control Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-14745 SN - 1438-0064 ER -